Question

3. A picture frame has its length 8 cm longer than its width. It has an inner
1-cm boundary such that a maximum 660 cm2-picture may fit into it. Find
the dimensions of this frame.?​

Answer 1

Given:

A picture frame has its length 8 cm longer than its width.

It has an inner  1-cm boundary such that a maximum 660 cm2-picture may fit into it

To find:

Find  the dimensions of this frame?​

Solution:

Let's assume,

"L" → the length of the picture frame

"W" → the width of the picture frame

Since the picture frame has its length 8 cm longer than its width, so we can form an equation as,

L = W + 8

The picture frame has an inner boundary of 1 cm, so,

The length of the picture = [L - (2×1)] = [W + 8 - 2] = [W + 6]

The width of the picture = [W - (2×1)] = [W - 2]

The area of the picture which may fit into the frame = 660 cm²

We know the formula of the area of the rectangle is,

$\boxed{\bold{Area\:of\:the\:rectangle = length \times breadth}}$

Therefore, we can form an equation as,

[Length of the picture] × [Width of the picture] = [Area of the picture]

$\implies [W+6][W-2] = 660$

$\implies W^2 + 6W -2W - 12 = 660$

$\implies W^2 + 4W - 12 = 660$

$\implies W^2 + 4W - 672 = 0$

$\implies W^2 - 24W + 28W - 672 = 0$

$\implies W(W - 24) + 28(W - 24) = 0$

$\implies (W - 24)(W + 28) = 0$

$\implies W = 24 \:or\:W = -28$

the value of width cannot be negative, so ignoring the negative value

$\implies \bold{W = 24\:cm}$ ← width of the picture frame

∴ L = W + 8 = 24 + 8 = 32 cm ← length of the picture frame

Thus, the dimension of this picture frame is → 32 cm × 24 cm.

-----------------------------------------------------------------------------------------------

Also View:

A square picture frame has sides of 0.7 meters. If the cost of a coloured paper is 20 per meter, what is the cost of putting coloured paper around the frame

https://brainly.in/question/7457014

A rectangle picture frame is 54 cm long and 36 cm wide. What will be the length of the wooden frame required to make it.

https://brainly.in/question/2058343

Rani has a photo frame without a photo in the shape of a triangle with sides a,b,c in length. She wants  to find the perimeter of a triangle formed by joining the mid-points of the sides of the photo-frame.  She could not understand how to overcome this problem. /she shares this problem with her Sonia.  Sonia helps her and the required perimeter is computed.

i) Find the perimeter of the triangle formed by joining the mid-points of the frame.

ii) Which mathematical concept is used in the above problem?

https://brainly.in/question/8455091

The dimensions of a photograph are 30 cm into 20 cm what length of the wooden frame is needed to frame the picture​?

https://brainly.in/question/13298188